Divide the following complex numbers: $\dfrac{7 e^{13\pi i / 12}}{ e^{11\pi i / 12}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $7 e^{13\pi i / 12}$ ) has angle $\frac{13}{12}\pi$ and radius 7. The second number ( $ e^{11\pi i / 12}$ ) has angle $\frac{11}{12}\pi$ and radius 1. The radius of the result will be $\frac{7}{1}$ , which is 7. The angle of the result is $\frac{13}{12}\pi - \frac{11}{12}\pi = \frac{1}{6}\pi$ The radius of the result is $7$ and the angle of the result is $\frac{1}{6}\pi$.